| dMafart_model {bioinactivation} | R Documentation |
First Derivate of the Weibull-Mafart Model
Description
Calculates the first derivative of Weibull-Mafart model at a given time for the model parameters provided and the environmental conditions given.
Usage
dMafart_model(t, x, parms, temp_profile)
Arguments
t |
numeric vector indicating the time of the experiment. |
x |
list with the value of N at t. |
parms |
parameters for the secondary model. No explicit check of their validity is performed (see section Model Parameters). |
temp_profile |
a function that provides the temperature at a given time. |
Details
The model is developed from the isothermal Weibull-Mafart model without
taking into
account in the derivation the time dependence of \delta_T for
non-isothermal temperature profiles.
This function is compatible with the function
predict_inactivation.
Value
The value of the first derivative of N at time t as a list.
Model Equation
\frac{dN}{dt} = -N \cdot p \cdot (1/\delta)^p \cdot t^{p-1}
\delta(T) = \delta_{ref} \cdot 10^{- (T-T_ref)/z}
Model Parameters
temp_ref: Reference temperature for the calculation.
delta_ref: Value of the scale factor at the reference temperature.
z: z-value.
p: shape factor of the Weibull distribution.
Note
For t=0, dN = 0 unless n=1. Hence, a small shift needs to be introduced to t.